Part of the kalam cosmological argument draws upon the claim that an actual infinite cannot exist. Classical theists also maintain both that some individuals will earn eternal life and that God infallibly foreknows the future. The claim that these latter two theses do not require that an actual infinite exists because God possesses an intuitive, rather than propositional intellect, is examined and rejected. Although the future is potential, rather than actual, classical theism requires that the (...) future be, in a sense, actually infinite. (shrink)

Cosmological arguments attempt to prove the existence of God by appeal to the necessity of a first cause. Schematically, a cosmological argument will thus appear as: (1) All contingent beings have a cause of existence. (2) There can be no infinite causal chains. (3) Therefore, there must be some non-contingent First Cause. Cosmological arguments come in two species, depending on their justification of the second premiss. Non-temporal cosmological arguments, such as those of Aristotle and Aquinas, view causation (...) as requiring explanatory or conceptual priority, and thus insist that there can be no infinite regresses in such priority. Temporal cosmological arguments, also called kalam cosmological arguments due to their historical roots in Islamic kalam philosophers such as Abu Yusuf Ya'qub b. Ishaq al-Kindi and Abu Ali al-Hussain ibn Sina, view causation as requiring temporal priority, and thus insist that there can be no infinite temporal regresses.1 The kalam cosmological argument thus requires some supporting argument showing the incoherence of an infinite temporal regress of causally related events. William Lane Craig, in "The Finitude of the Past and the Existence of God"2, attempts to provide such an argument: (4) An actual infinite cannot exist. (5) An infinite temporal regress of events is an actual infinite. (6) Therefore an infinite temporal regress of events cannot exist. (9) I will not be concerned here with the general status of cosmological arguments, kalam or otherwise, or with contesting Craig's assumption that an infinite past would (unlike an infinite future) constitute a problematic actual infinity. I am rather concerned with Craig's general working principle, embodied in (4) above, that actual infinities are impossible. Craig, of course, is not alone in denying the possibility of the actually infinite. Resistance to such infinities is at least as old as Aristotle (Physics 3.5.204b1 – 206a8), and, as Craig rightly points out, persists through much of modern (i.e., post-scholastic, pre-twentieth-century) philosophy.. (shrink)

It is commonly assumed that Aristotle denies any real existence to infinity. Nothing is actually infinite. If, in order to resolve Zeno’s paradoxes, Aristotle must talk of infinity, it is only in the sense of a potentiality that can never be actualized. Aristotle’s solution has been both praised for its subtlety and blamed for entailing a limitation of mathematic. His understanding of the infinite as simply indefinite (the “bad infinite” that fails to reach its accomplishment), his (...) conception of the cosmos and even its prime mover as finite (in the sense of autarchic/self-contained) have been contrasted with the subsequent claim of God as ens infinitum (understood as a “positive” infinity). The goal of this essay is to reexamine the major texts (notably De caelo) and to demonstrate that (1) Aristotle’s claim according to which there is no actual infinite concerns only substances, not processes. (2) That Aristotle does not deny an actual infinite as such. (3) That when considering time and God (qua eternal) Aristotle acknowledges an actual infinite. (shrink)

"This article presents an analysis of William Lane Craig’s argument of the finitude of the past based on the impossibility of the formation of an actual infinite. To achieve the aim of this academic work we use, as a primary base, a book written by Craig called Reasonable Faith: Christian Truth and Apologetics and a chapter written by the same author along with James Sinclair called The Kalam Cosmological Argument in The Blackwell Companion to Natural Theology. These works, (...) in our opinion, provide sufficient primary material to study the topic. However, other articles and books by Craig are also referenced, and the commentaries of some other authors, who deal with this problem, are also used. Throughout this work, we consider the historical context and Craig’s incorporation of the kalam cosmological argument. We go on to analyse the presuppositions given by this author and consequently we study, progressively, the formulations that Craig himself made to reach his conclusion. /// Este artigo apresenta uma análise do argumento de William Lane Craig sobre a finitude do passado baseado na impossibilidade da formação de um infinito atual. Para atingir o objetivo deste trabalho acadêmico, utilizamos como fonte primária uma obra escrita pelo próprio Craig, intitulada Fé racional: verdade cristã e apologética, e um capítulo escrito pelo mesmo autor em colaboração com James Sinclair chamado O argumento cosmológico kalam, em The Blackwell Companion to Natural Theology. Estes trabalhos, em nossa opinião, oferecem suficientes elementos para o estudo do tópico. Entretanto, outros artigos e livros de Craig também foram citados, bem como os comentários de vários autores que tratam do problema. No decorrer deste trabalho consideramos o contexto histórico e a incorporação de Craig ao argumento cosmológico kalam. Mais adiante, analisamos primeiramente os pressupostos dados pelo mencionado autor e, em consequência, estudamos progressivamente as formulações feitas pelo próprio Craig para obter suas conclusões. ". (shrink)

It has often been thought that the existence of an infinite amount of time implies the realization of all possibilities. However, it can be proved that it is not true that for any T, if T is an infinite period of time, then every possibility is actualized in T. The proof works for any sense of 'possibility' in which there are possibilities that cannot be actualized simultaneously.It still might be argued that if there is an infinite (...) amount of time, then each possibility is actualized sometime (during some infinite period of time, though not all). In particular it might be claimed that if there is an infinite amount of time, then there is an uninterrupted infinite period of time; and (P*) for any T, if T is an uninterrupted infinite period of time, then every possibility is actualized in T. However, it can also be shown that (P*) is not necessarily true.For it to be actually true, some very strong Principle of Universal Random Change must be true. (shrink)

ABSTRACT W.L. Craig has argued that the universe has a beginning because (1) the infinitude of the past entails the existence of actual infinite multitudes of past intervals of time, and (2) the existence of actual infinite multitudes is impossible. Puryear has rejected (1) and argued that what the infinitude of the past entails is only the existence of an actual infinite magnitude of past time. But this does not preclude the (...) infinitude of the past, Puryear claims, because there can be no justification for the claim that actual infinite magnitudes are impossible. I argue, against Puryear, that there can be such a justification. I claim, nevertheless, that, for reasons entirely different from Puryear’s, the finitude of the past cannot be established based either on the impossibility of actual infinite multitudes or on the impossibility of actual infinite magnitudes. My arguments in this paper draw on insights from al-Kindī and Avicenna. (shrink)

W.L. Craig has argued that the universe has a beginning because (1) the infinitude of the past entails the existence of actual infinite multitudes of past intervals of time, and (2) the existence of actual infinite multitudes is impossible. Puryear has rejected (1) and argued that what the infinitude of the past entails is only the existence of an actual infinite magnitude of past time. But this does not preclude the infinitude (...) of the past, Puryear claims, because there can be no justification for the claim that actual infinite magnitudes are impossible. I argue, against Puryear, that there can be such a justification. I claim, nevertheless, that, for reasons entirely different from Puryear’s, the finitude of the past cannot be established based either on the impossibility of actual infinite multitudes or on the impossibility of actual infinite magnitudes. My arguments in this paper draw on insights from al-Kindī and Avicenna. (shrink)

I argue that animals have rights in the sense of having valid claims, which might turn out to be actual rights as society advances and new scientific-technological developments facilitate finding alternative ways of satisfying our vital interests without using animals. Animals have a right to life, to liberty in the sense of freedom of movement and communication, to subsistence, to relief from suffering, and to security against attacks on their physical existence. Animals’ interest in living, freedom, subsistence, and (...) security are of vital importance to them, and they do not belong to us; they are not the things we have already possessed by virtue of our own nature. (shrink)

InMetaphysicsΘ.6, 1048b14-17, Aristotle treats the problem of what it is for the infinite to exist potentially, i.e. to be potentially actual. According to my interpretation, Aristotle argues that to exist potentially is for the infinite to have a potentiality which cannot be actualized in reality but only in thought, because it is a potentiality the process of whose actualization cannot be brought to an end.

In this article, I discuss Leibniz's interpretation of the cosmological argument for the existence of God. In particular, I consider whether Leibniz's position on this point was developed partly in reference to Spinoza's position. First, I analyze Leibniz's annotations from 1676 on Spinoza's Letter 12. The traditional cosmological argument, as found in Avicenna and Saint Thomas for example, relies on the Aristotelian assumption that an actual infinite is impossible and on the idea that there can be no (...) effect without a cause. From these premises, the argument concludes that God must be the uncaused first cause of all things. In Letter 12, Spinoza follows Chasdai Crescas and rejects this proof. Instead, he develops a variant of the cosmological argument which depicts God as the self-caused ground of all causes or things. In his annotations, Leibniz agrees with Spinoza about the inadequacy of the traditional argument, but remains ambiguous as to Spinoza's conception of God as a self-caused being. Next, I turn to Leibniz's comments from 1678 on Spinoza's Ethics. Here, Leibniz develops an original interpretation of the cosmological argument based entirely on the consideration of conceptual relations. Leibniz's argument depicts God as an uncaused being conceived through itself which is the condition of conceivability of all things. I argue that Leibniz developed this argument in deliberate opposition to Spinoza's conception of God as the self-caused ground of all causes or things. (shrink)

In this article, I discuss Leibniz’s interpretation of the cosmological argument for the existence of God. In particular, I consider whether Leibniz’s position on this point was developed partly in reference to Spinoza’s position. First, I analyze Leibniz’s annotations from 1676 on Spinoza’s letter 12. The traditional cosmological argument, as found in Avicenna and Saint Thomas for example, relies on the Aristotelian assumption that an actual infinite is impossible and on the idea that there can be no (...) effect without a cause. From these premises, the argument concludes that God must be the uncaused first cause of all things. In letter 12, Spinoza follows Chasdai Crescas and rejects this proof. Instead, he develops a variant of the cosmological argument which depicts God as the self-caused ground of all causes or things. In his annotations, Leibniz agrees with Spinoza about the inadequacy of the traditional argument, but remains ambiguous as to Spinoza’s conception of God as a self-caus. (shrink)

In this article, we evaluate various responses to a noteworthy objection, namely, the infinite God objection to the kalām cosmological argument. As regards this objection, the proponents of the kalām argument face a dilemma—either an actual infinite cannot exist or God cannot be infinite. More precisely, this objection claims that God’s omniscience entails the existence of an actual infinite with God knowing an actually infinite number of future events or abstract objects, such (...) as mathematical truths. We argue, however, that the infinite God objection is based on two questionable assumptions, namely, that it is possible for an omniscient being to know an actually infinite number of things and that there exist an actually infinite number of abstract objects for God to know. (shrink)

We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous (...) terms. That is, could there be longer than infinite lengths or temporal durations? We argue that the answer is surprisingly yes, and we outline the properties of a number system that could be employed to characterize such magnitudes. (shrink)

Most philosophers have given up George Berkeley’s proof for the existence of God as a lost cause, for in it, Berkeley seems to conclude more than he actually shows. I defend the proof by showing that its conclusion is not the thesis that an infinite and perfect God exists, but rather the much weaker thesis that a very powerful God exists and that this God’s agency is pervasive in nature. This interpretation, I argue, is consistent with the texts. (...) It is also an important component of Berkeley’s philosophical project, which consists of launching many small arguments against his philosophical and theological opponents. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Martin Heidegger and OntologyEmmanuel Levinas (bio)The prestige of Martin Heidegger 1 and the influence of his thought on German philosophy marks both a new phase and one of the high points of the phenomenological movement. Caught unawares, the traditional establishment is obliged to clarify its position on this new teaching which casts a spell over youth and which, overstepping the bounds of permissibility, is already in vogue. For once, (...) Fame has picked one who deserves it and, for that matter, one who is still living. Anyone who has studied philosophy cannot, when confronted by Heidegger’s work, fail to recognize how the originality and force of his achievements, stemming from genius, are combined with an attentive, painstaking, and close working-out of the argument—with that craftsmanship of the patient artisan in which phenomenologists take such pride. In this study, it is important for us to understand, above all, the true intentions of our author, to illuminate what he thinks really needs to be said, and to surmise what is most critical for him.To get to the heart of Heidegger’s system, it seems fitting to begin with a problem that is generally familiar. We choose the problem of knowledge, a deeper understanding of which takes us to the very threshold of Heidegger’s thought. For this problem, central to modern philosophy, is one of the main obstacles of modern philosophy that Heidegger wishes to surmount. Neo-Kantianism, which takes knowledge as the philosophical problem of the first rank, is the movement against which Heidegger rebels with all his strength. We have, thus, every chance of gaining access to his thought by the main door, so to speak. Once inside the system we will try to trace its outlines, 2 reserving, for a second part of our work, the determination of Heidegger’s place in the history of ideas, especially in the phenomenological movement, as well as of his relations with the philosopher to whom he owes so much—Edmund Husserl. 31In its most general form, the problem of the theory of knowledge has a critical significance. It consists in delineating a domain where knowledge can be certain and in determining the criteria for the legitimate scope of knowledge. But this problem, as normal and as simple as it may appear, has deeper roots. That knowledge should need a criterion at all presupposes that truth is not identical to all that is known and that the course [End Page 11] of things can fail to correspond with the course of thought. “How does knowledge correspond to being?” is a more profound formulation of the problem of knowledge.But we are not going to touch anymore on the primordial phenomenon that generates the problem. The problem of correspondence between thing and thought presupposes a free activity of thought and its isolation in relation to the object. It is precisely this presupposition which renders their harmony and even their contact problematic. “How does the subject take leave of itself to attain the object?” is what the problem of knowledge, in the last analysis, boils down to. Its true source is thus the concept of “subject” as elaborated by modern philosophy. The cogito presided over the subject’s birth. The cogito was the affirmation of the privileged nature of the subject’s immanent sphere, of its unique place in existence; hence, the cogito was the specificity of the subject’s connection to the rest of reality, the sui generis nature which opens up the passage from immanence to transcendence, the passage from ideas contained in the thinking substance to 4 their “formal existence.”The concept of the subject, understood as a substance having a specific position in the entire domain of being, presents us with difficulties of two kinds. First, how do we understand this leave-taking from the self which the thinking substance brings about and which displays an entirely original aspect? Indeed, we could say that thought, in reaching out toward objects, does not actually take leave of itself, since its objects—considered as ideas and contents of thought—are, in a certain sense, already within it. In order to make sense of this paradox, Descartes... (shrink)

I conceive of Spinoza’s substance monism as a response to Aristotle’s prohibition against actual infinity for one key reason: nature, being all things, is necessarily infi nite. Spinoza encapsulates his substance monism with the phrase, “Deus sive Natura,” implying that there is only one infinite substance, which also possesses an infi nity of attributes, of which we are but modes. These logical delineations of substance never actually break up God’s reality. Aristotle’s well-known argument against the reality of an (...) actual infinity in his Physics prohibits the existence of an actually infinite bodily substance because it would necessarily “destroy” (Physics 204b26-27) all other elements or bodies. On Aristotle’s view, there is a fundamental and concrete distinction between things: each substance is primarily a this (Categories 3b10). I maintain that Spinoza’s rationalism and radicalization of the principle of sufficient reason lends him greater explanatory potential than Aristotle to justify the (non) existence of actual infinity. (shrink)

In this paper I shall “draw” a sketch of a version of Meinongian Presentism. After having briefly presented some data that presentists need to explain and three problems that typically affect presentism (the triviality objection, the problem of the reference of true propositions’ constituents that seem to involve merely past and merely future objects, the truthmaking problem), I shall clarify the bases of my theory. First, I shall reject the actualist presentist assumption, according to which there are no things that (...) do not exist now. Secondly, I shall introduce some notions (e.g., the ones of tensed properties and of temporal existence) that will be useful in order to clarify the contrast between eternalist and non-eternalist metaphysical theories of time. Thirdly, I shall define Meinongian Presentism. Finally, I shall try to demonstrate that this version can deal with the aforementioned problems and with the presentist data in a serious and perspicuous way. (shrink)

the meditations on first philosophy presents us with an alleged proof for the existence of God that proceeds from the existence of an idea of an infinite being in the human mind—an idea of God—to the existence of God himself. Insofar as we have an idea of an infinite being, an idea with “infinite objective reality,” we can legitimately ask whence it came to us. The only possible cause of this idea, claims Descartes, is (...) an infinite being, namely, God. The occurrence of just this idea in the proof is essential. In fact, Descartes maintains that any such causal proof for God’s existence crucially relies on this idea: “it seems to me that all these proofs based on his effects are reducible to a single one; and also .. (shrink)

In this paper I attempt to trace the development of Gottfried Leibniz’s early thought on the status of the actually infinitely small in relation to the continuum. I argue that before he arrived at his mature interpretation of infinitesimals as fictions, he had advocated their existence as actually existing entities in the continuum. From among his early attempts on the continuum problem I distinguish four distinct phases in his interpretation of infinitesimals: (i) (1669) the continuum consists of assignable points (...) separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no gaps between them; (iii) (1672-75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus); (iv) (1676 onward) infinitesimals are fictitious entities, which may be used as compendia loquendi to abbreviate mathematical reasonings; they are justifiable in terms of finite quantities taken as arbitrarily small, in such a way that the resulting error is smaller than any pre-assigned margin. Thus according to this analysis Leibniz arrived at his interpretation of infinitesimals as fictions already in 1676, and not in the 1700's in response to the controversy between Nieuwentijt and Varignon, as is often believed. (shrink)

Most interpreters hold that Kant rejects actually infinite tota synthetica as conceptually impossible. This view is attributed to Kant to relieve him of the charge that the first antinomy’s thesis argument presupposes transcendental idealism. I argue that important textual evidence speaks against this view, and Kant in fact affirms the conceptual possibility of actually infinite tota synthetica. While this means the first antinomy may not be decisive as an indirect argument for idealism, it gives us a better account (...) of how our ideas of the unconditioned generate the antinomies, and it allows us to see important and often overlooked elements in Kant’s account of the infinite. (shrink)

Modal Meinongianism provides the semantics of sentences involving intentional verbs Priest. To that end, Modal Meinongianism employs a pointed non-normal quantified modal logic model. Like earlier Meinongian views Modal Meinongianism has a characterisation principle, that claims that any condition whatsoever is satisfied by some object in some world. Recently, Everett has proposed an argument against QCP that, if successful, gives rise to problems identical to those Russell raised for Naïve Meinongianism, namely that it allows for true contradictions, and allows us (...) to define anything into existence. Everett claims that the ordinary meanings of “actual” license an inference pattern, such that if an object satisfies Actual A at some world, then that object satisfies A in the actual world. Given that actual world is the designated point of evaluation for truth simpliciter, QCP would fall prey to Russell’s criticisms. As opposed to Everett, I argue that, even if we grant Everett the assumption that “actual” is a modal indexical that rigidly refers to the actual world, it does not conform to the inference pattern above. This is because when an object satisfies Actual A at some world, this alters the assertoric force of “actual”, because “actual” is interpreted in the scope of some modal or intentional operator. I also explain that Everett’s proposed example carries existential commitment because the problematic noun-phrase occurs outside the scope of a modal or intentional operator. (shrink)

In a series of much discussed articles and books, William Lane Craig defends the view that the past could not consist in a beginningless series of events. In the present paper, I cast a critical eye on just one part of Craig's case for the finitude of the past – viz. his philosophical argument against the possibility of actually infinite sets of objects in the ‘real world’. I shall try to show that this argument is unsuccessful. I shall also (...) take a close look at several considerations that are often thought to favour the possibility of an actual infinite, arguing in each case that Craig's response is inadequate. (shrink)

The seventeenth century was an important period in the conceptual development of the notion of the infinite. In 1643, Evangelista Torricelli (1608-1647)—Galileo’s successor in the chair of mathematics in Florence—communicated his proof of a solid of infinite length but finite volume. Many of the leading metaphysicians of the time, notably Spinoza and Leibniz, came out in defense of actual infinity, rejecting the Aristotelian ban on it, which had been almost universally accepted for two millennia. Though it would (...) be another two centuries before the notion of the actually infinite was rehabilitated in mathematics by Dedekind and Cantor (Cauchy and Weierstrass still considered it mere paradox), their impenitent advocacy of the concept had significant reverberations in both philosophy and mathematics. In this essay, I will attempt to clarify one thread in the development of the notion of the infinite. In the first part, I study Spinoza’s discussion and endorsement, in the Letter on the Infinite (Ep. 12), of Hasdai Crescas’ (c. 1340-1410/11) crucial amendment to a traditional proof of the existence of God (“the cosmological proof” ), in which he insightfully points out that the proof does not require the Aristotelian ban on actual infinity. In the second and last part, I examine the claim, advanced by Crescas and Spinoza, that God has infinitely many attributes, and explore the reasoning that motivated both philosophers to make such a claim. Similarities between Spinoza and Crescas, which suggest the latter’s influence on the former, can be discerned in several other important issues, such as necessitarianism, the view that we are compelled to assert or reject a belief by its representational content, the enigmatic notion of amor Dei intellectualis, and the view of punishment as a natural consequent of sin. Here, I will restrict myself to the issue of the infinite, clearly a substantial topic in itself. (shrink)

Defenders of the Kalām Cosmological Argument appeal to the so-called Hilbert’s Hotel Argument to establish the finitude of the past based on the impossibility of actual infinites. Some of their opponents argue that this proves too much because if the universe cannot be beginningless due to the impossibility of actual infinites, then, for the same reason, it cannot be endless either. Discussing four different senses of the existence of an actual infinite, I criticize both sides (...) of the debate by showing, on the one hand, that the Hilbert’s Hotel Argument is not powerful enough to rule out the possibility of the infinitude of the past and, on the other hand, that the soundness of the argument for the finitude of the past from the impossibility of actual infinites does not establish the soundness of the parallel argument for the finitude of the future. (shrink)

The paper begins with an exposition of Aristotle’s own philosophy of mathematics. It is claimed that this is based on two postulates. The first is the embodiment postulate, which states that mathematical objects exist not in a separate world, but embodied in the material world. The second is that infinity is always potential and never actual. It is argued that Aristotle’s philosophy gave an adequate account of ancient Greek mathematics; but that his second postulate does not apply to modern (...) mathematics, which assumes the existence of the actual infinite. However, it is claimed that the embodiment postulate does still hold in contemporary mathematics, and this is argued in detail by considering the natural numbers and the sets of ZFC. (shrink)

Before establishing his mature interpretation of infinitesimals as fictions, Gottfried Leibniz had advocated their existence as actually existing entities in the continuum. In this paper I trace the development of these early attempts, distinguishing three distinct phases in his interpretation of infinitesimals prior to his adopting a fictionalist interpretation: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with (...) no gaps between them; (iii) (1672- 75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus). In 1676, finally, Leibniz ceased to regard infinitesimals as actual, opting instead for an interpretation of them as fictitious entities which may be used as compendia loquendi to abbreviate mathematical reasonings. (shrink)

Infinity exists as a concept but has no existence in actuality. For infinity to have existence in actuality either time or space have to already be infinite. Unless something is already infinite, the only way to become infinite is by an 'infinity leap' in an infinitely small moment, and this is not possible. Neither does infinitely small have an existence since anything larger than zero is not infinitely small. Therefore infinity has no existence (...) in actuality. (shrink)

This book offers a discussion of the kalām cosmological argument, and presents a defence of a version of that argument after critically evaluating three of the most important versions of the argument. It argues that, since the versions of the kalām cosmological argument defended by Philoponus (c. 490–c. 570), al-Ghazālī (1058– 1111), and the contemporary philosopher, William Lane Craig, all deny the possibility of the existence of an actual infinite, these arguments are incompatible with Platonism and the (...) view that God foreknows an endless future. This conclusion, however, is not a problem for the proponents of the kalām cosmological argument, for the book shows how the argument can be defended without denying the possibility of the actual infinite. -/- In order to offer a comprehensive analysis of Philoponus and al-Ghazālī’s cosmological arguments, the book draws on recent English translations of some of their works. Next, the book advances a detailed argument against the popular argument based on the impossibility of an actual infinite. Finally, the book offers a unique defence of the kalām cosmological argument by defending philosophical arguments for a beginning of time that do not deny the actual infinite, evaluating which hypothesis best explains the discoveries of modern cosmology, and offering an argument in support of the premise that, if the universe came into existence, then God brought it into existence. (shrink)

One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series (...) must have a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite. (shrink)

This chapter contains sections titled: Introduction Did the Universe Begin to Exist? Everything That Begins to Exist Has a Cause The Cause of the Universe Properties of the First Cause Objections Conclusion References.

One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series (...) must have a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite. (shrink)

Aggregative consequentialism and several other popular moral theories are threatened with paralysis: when coupled with some plausible assumptions, they seem to imply that it is always ethically indifferent what you do. Modern cosmology teaches that the world might well contain an infinite number of happy and sad people and other candidate value-bearing locations. Aggregative ethics implies that such a world contains an infinite amount of positive value and an infinite amount of negative value. You can affect only (...) a finite amount of good or bad. In standard cardinal arithmetic, an infinite quantity is unchanged by the addition or subtraction of any finite quantity. So it appears you cannot change the value of the world. Modifications of aggregationism aimed at resolving the paralysis are only partially effective and cause severe side effects, including problems of “fanaticism”, “distortion”, and erosion of the intuitions that originally motivated the theory. Is the infinitarian challenge fatal? (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume Studies Volume XXIII, Number 2, November 1997, pp. 227-244 Hume on Geometry and Infinite Divisibility in the Treatise H. MARK PRESSMAN Scholars have recognized that in the Treatise "Hume seeks to find a foundation for geometry in sense-experience."1 In this essay, I examine to what extent Hume succeeds in his attempt to ground geometry visually. I argue that the geometry Hume describes in the Treatise faces a (...) serious set of problems. Geometric Lines Hume maintains that ideas "are images" (T 6) which may be called up "when I shut my eyes" (T 3). "That we may fix the meaning of a word, figure," according to Hume, "we may revolve in our mind the ideas of circles, squares, parallelograms, triangles of different sizes and proportions, and may not rest on one image or idea" (T 22). As Arthur Pap notes, "'Idea' is in Hume's usage synonymous with 'mental image'." D.C.G. MacNabb also notes that "Hume thought of ideas as images, and primarily as visual images."2 When Hume argues, then, that "we have the idea of indivisible points, lines and surfaces conformable to the [geometer's] definition" (T 44), he is arguing that we have mental images of geometry's points, lines and planes. Consider geometric lines first. Geometers define a line "to be length without breadth or depth" (T 42). It is not apparent to everyone that we have mental images of such lines. According to "L'Art de penser" (T 43), published in 1662, it is impossible "to conceive a length without any breadth" (T 43). H. Mark Pressman is at the Department of Philosophy, University of California, Davis, 1238 Social Sciences and Humanities Building, Davis CA 95616-8673 USA. email: [email protected] 228 H. Mark Pressman We can only by an abstraction "consider the one without regarding the other" (T 43). Hume, however, offers "clear proof" (T 44), in the form of two arguments, that we actually possess ideas or mental images of geometry's lines. First, we have ideas or mental images of lengths with breadth, though these are supposed never to be without breadth and thus not geometric lines. (A mental image oflength is also a mental image with length, just as "to say the idea of extension agrees to any thing, is to say it is extended" [T 240].) Hume reduces to absurdity the view that our mental images of length are always with breadth and thus not images of geometric lines. If our length-images were always with breadth, then our mental images would be endlessly divisible in breadth, since they would always have some positive breadth (T 43). But no mental image is endlessly divisible, for the mind arrives "at an end in the division of its ideas, nor are there any possible means of evading the evidence of this conclusion" (T 27). We thus have an idea or image of length without (divisible) breadth conforming to the geometer's definition (T 44). Second, we can imagine or picture the termination of a geometric plane. But a geometric plane must terminate in a geometric line (T 44). (Proof: Assume L is a line with breadth which terminates plane P. Since L has breadth, L must contain at least two parts, w and y, exactly one of which actually terminates P. But whether it is w or y, L doesn't terminate P, which was the assumption.) Since we can picture the termination of a geometric plane, we can picture a geometric line, length without divisible breadth. It is one thing to have ideas or mental images of geometric lines which may be called up "when I shut my eyes" (T 3). It is another for such objects actually to exist "in nature." The conceptualist holds that though (a) geometry 's points, lines and planes are ideas, nevertheless (b) there are no such things in nature and that (c) there can't be such things in nature: [T]he objects of geometry... are mere ideas in the mind, and not only never did, but never can exist in nature. They never did exist; for no one will pretend to draw a line or make a... (shrink)

I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not, I do not say divisible, but actually divided; and consequently the least particle ought to be considered as a world full of an infinity (...) of different creatures. (shrink)

Jean Mair, au début du XVIe siècle, entreprend de montrer que linfini existe en acte. Son traité De l'Infini prolonge les débats du XIVe siècle sur l'infini et le continu. Le problème de l' infini y est traité d'une manière principalement logique. L'infini est un terme qui a plusieurs sens selon son usage dans des propositions. La distinction centrale est celle de l'infini au sens catègorématique et de l'infini au sens synatégorématique. Mais si les auteurs du XIVe siècle admettent tous (...) l'infini au sens syncatêgorématique, la plupar récusent l'être en acte de l' infini au sens catègorématique. C'est à ce dernier point que Jean Mair consacre l'essentiel de sa réflexion. A l'intérieur d'un cadre qui reste aristotélicien par sa problématique d'ensemble et la formulation des questions, il renverse, grâce aux outils conceptuels de la logique terministe, une thèse centrale dans l'aristotélisme. Son traité contribue ainsi à développer l'idée que l'infini peut exister dans la nature. At the beginning of the 16th Century, Jean Mair set out to prove that the infinite exists Hot just potentially but actually. His treatise Propositum de infinito prolonged the 14th Century debates over the infinite and continuity, and it dealt logically with the problem of the infinite. The infinite is a term that has several meanings, depending upon its usage in propositions. The distinction between the categorematic and syncategorematic infinites is the central one in the treatise. If 14th Century authors by and large accepted the syncategorematic infinite, the majority challenged the existence of an actual infinite in the case of the categorematic infinite. Jean Mair devoted the bulk of his reflections to the latter situation. Within a framework that remained thoroughly Aristotelian, both in his overall problematic, as well as in the way he formulated questions, Mair overturned a central Aristotelian thesis, with the aid of conceptual tools from terminist logic. In this way his treatise contributed to the development of the idea that the infinite can exist in nature. (shrink)

The thesis that existence is radically different from the determinacy of an actually existing thing –Kant considers this thesis to be the unsurmountable objection against the cosmological and the ontological argument– is the same thesis that demands a specific explanation of the existence of that actually existing thing. The notion of existence that results from its complete exclusion from the realm of the contents thoroughgoing determined by real predicates requires, thus, precisely because this thoroughness excludes it, a (...) specific reason that explains that in the actually existing thing its own actual existence is in fact united with its own determinacy; that notion of existence, however, cancels at the same time the requirement of a sufficient reason of the existence of what actually exists, and again for the same reason, namely, because since existence is as such excluded from the determinacy of the existing things, it radically differs from the specific realm where determinacy is constituted (that is why existing things are thoroughgoing determined as possible), and, therefore, it invalidates any application to itself of the logical laws that are valid only for the merely possible domain of determinacy. (shrink)

I show the inadequacy of whitrow's recent argument ("british journal for the philosophy of science", Volume 29, Pages 39-45) against the possibility of an infinite past. I argue that it is impossible to prove "a priori" the non-Existence of an infinite past or future.

The aim of this paper is to present a proof to the conclusion that is impossible to traverse an infinite series (in particular, an infinite series of past moments). This may also show (given additional assumptions) that the series of past moments cannot be infinite. In the first section I formulate five theses concerning traversing, successive addition and successive subtraction and I present the idea of the argument: if it were possible to traverse an infinite past, (...) it should be in principle possible to go back, which is, however, impossible. The main body of the paper is concerned with working out a simple mathematical representation of some structural features of processes like traversing and successive addition. I also make a crucial distinction between completion of a process at a particular time and its timeless "completion" in infinite time. In section V, I present the formal proof and defend it against a possible objection of question-begging. Finally, I suggest that my argume. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Negotiating Maternal IdentityAdrienne Rich’s Legacy for Inquiry into the Political-Philosophical Dimensions of Pregnancy and ChildbirthCandace JohnsonGiving birth has been described as the crossing of an imaginary threshold, which separates an independent maternal self from some sort of dual or subordinate existence. The metaphor of a border has also been employed to demonstrate this transformation, which may be liberating, oppressive, or some complex combination thereof (Weir 2006; Martinez 2004). (...) What happens, in psychic and sociopolitical terms, in the journey across this border? Can a woman, as an independent, autonomous being, preserve her identity, her selfhood as a mother? Is the transition to motherhood an expression of culture or nature? The answers to these questions are infinitely complex, yet are at the core of philosophical, political, and personal explorations of the maternal. Central to these explorations are academic critiques and personal responses to the biomedical mediation of the transition to motherhood. For some women, medical intervention in pregnancy and childbirth is inherently oppressive, whereas for other women such intervention is a marker of privilege. In a groundbreaking volume published in 1998, Margaret Lock and Patricia Kaufert argue that women respond to different biomedical interventions in pragmatic ways, which reflect their lived experiences. They claim that “it is more appropriate to understand women’s responses in medical settings as reflecting their daily experiences as part of a domestic group, a community, or a society” (19). [End Page 65]I would like to advance this analysis by suggesting that women respond to biomedical intervention in pregnancy and childbirth in ways that reflect not simply their practical needs and realities, but important details about inequality and identity. Women’s relative degrees of power and agency in society are expressed through their preferences for care during pregnancy and childbirth. In addition, and in connection with the (structural) dynamics of inequality, these preferences reflect the complexities of shifting, negotiated, maternal identities. In order to consider the ways in which women negotiate maternal identity through their preferences concerning care during pregnancy and childbirth, I will examine the contributions of Adrienne Rich, which effectively serve as the foundation for this and countless other areas of women’s and gender studies. In Of Woman Born, Rich dedicates two full chapters to childbirth, and explains in these chapters that the institution of childbirth has come to dominate and eclipse women’s experiences. Moreover, the patriarchal circumscription of childbirth is reinforced by the isolation of childbirth (and motherhood) from other life events. Rich demonstrates these problems through the metaphor of “giving birth to oneself ” (29), which has (at least) two distinct meanings: self actualization and self replacement.My investigation into these meanings will include an examination of Rich’s philosophical treatment of pregnancy and childbirth and an assessment of the sociopolitical implications of both conceptions of “giving birth to oneself.” I will then subject these conceptions to empirical testing, as Rich insists. Such empirical testing is crucial because the social and political dimensions of the institutions of childbirth and motherhood are complex and differ from one context to the next. Rich explains that[t]o hold power over others means that the powerful is permitted a kind of short-cut through the complexity of human personality. He does not have to enter intuitively into the souls of the powerless, or to hear what they are saying in their many languages, including the language of silence. Colonialism exists by virtue of this short-cut—how else could so few live among so many and understand so little?(65)This essay will avoid a similar shortcut often taken by theorists, which builds philosophical arguments without empirical support. The empirical cases to be considered in the context of philosophical debate include Canada, Honduras, and Cuba, and details of each case will be drawn from extensive interview data from a larger empirical study.1 In the Canadian context, resistance to the constraining effects of motherhood as institution is reduced to resistance to medical regulation of pregnancy and childbirth. The benefit indicated by this resistance is that women have found ways to expand their range of options and reinterpret the birthing event, thereby integrating it into other realms [End Page 66... (shrink)

In Physics, Aristotle starts his positive account of the infinite by raising a problem: “[I]f one supposes it not to exist, many impossible things result, and equally if one supposes it to exist.” His views on time, extended magnitudes, and number imply that there must be some sense in which the infinite exists, for he holds that time has no beginning or end, magnitudes are infinitely divisible, and there is no highest number. In Aristotle's view, a plurality cannot (...) escape having bounds if all of its members exist at once. Two interesting, and contrasting, interpretations of Aristotle's account can be found in the work of Jaako Hintikka and of Jonathan Lear. Hintikka tries to explain the sense in which the infinite is actually, and the sense in which its being is like the being of a day or a contest. Lear focuses on the sense in which the infinite is only potential, and emphasizes that an infinite, unlike a day or a contest, is always incomplete. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kant on the Method of MathematicsEmily Carson1. INTRODUCTIONThis paper will touch on three very general but closely related questions about Kant’s philosophy. First, on the role of mathematics as a paradigm of knowledge in the development of Kant’s Critical philosophy; second, on the nature of Kant’s opposition to his Leibnizean predecessors and its role in the development of the Critical philosophy; and finally, on the specific role of intuition (...) in Kant’s philosophy of mathematics. One of the points that I want to make is that recognizing the importance of these first two issues is essential to giving an adequate account of the third. That is, only by appreciating how Kant uses the example of mathematical knowledge, and in particular the objections he had to previous accounts of such knowledge, can we understand the philosophical role that he ascribes to intuition in his own account of mathematics.I don’t propose to explain the details of Kant’s philosophy of mathematics, but rather to compare his views on mathematics in the pre-Critical Prize Essay of 1764 to those of the Critique of Pure Reason, with the aim of showing how Kant’s doctrine of construction in pure intuition arises out of a combination of two factors: first, his attempt to ground the distinction between the respective methods of mathematics and philosophy, and second, his concern to defend the reality of mathematical knowledge against the views of those he called ‘the metaphysicians.’ The first factor demands an account of the certainty of mathematics, the second requires an account of its content. I shall argue that there is a possible conflict between Kant’s accounts of these features in the Prize Essay, a possibility which is finally ruled out only by means of the Critical doctrine of pure intuition. So I hope to show that there is a significant philosophical role for intuition in Kant’s account of mathematical knowledge (over and above the more logical role attributed to it on readings [End Page 629] such as those of Friedman, Beth, and Hintikka1) in reconciling the content of mathematics and its certainty.2. THE MATHEMATICIANS VS. THE METAPHYSICIANSThroughout his early writings, Kant appealed to the evidence and certainty of mathematics; his attitude towards metaphysics, however, underwent a dramatic shift. In the Physical Monadology of 1756, Kant asked how metaphysics and geometry can be united,[f] or the former peremptorily denies that space is infinitely divisible, while the latter, with its usual certainty, asserts that it is infinitely divisible. Geometry contends that empty space is necessary for free motion, while metaphysics hisses the idea off the stage. Geometry holds universal attraction or gravitation to be hardly explicable by mechanical causes but shows that it derives from the forces which are inherent in bodies at rest and which act at a distance, whereas metaphysics dismisses the notion as an empty delusion of the imagination [1:475–6].2He attempted in this work to reconcile the respective positions of metaphysics and geometry regarding infinite divisibility, thereby demonstrating that “it is neither the case that the geometer is mistaken nor that the opinion to be found among metaphysicians deviates from the truth” [1:480]. But in a series of works from 1762–3, Kant reveals a markedly different attitude towards metaphysics. For example, in “The only possible argument in support of a demonstration of the existence of God,” Kant says:the mania for method and the imitation of the mathematician, who advances with a sure step along a well-surfaced road, have occasioned a large number of such mishaps on the slippery ground of metaphysics. These mishaps are constantly before one’s eyes, but there is little hope that people will be warned by them, or that they will learn to be more circumspect as a result [2:71].In contrast, Kant describes the geometer as uncovering “with the greatest certainty” the most secret properties of that which is extended [2:70]. But the less conciliatory attitude to metaphysics comes out most clearly in Kant’s actual procedure in “The only possible argument.” In the Seventh Reflection, he presents an attempt to explain the origin of... (shrink)

Between 1653 and 1655 Margaret Cavendish makes a radical transition in her theory of matter, rejecting her earlier atomism in favour of an infinitely-extended and infinitely-divisible material plenum, with matter being ubiquitously self-moving, sensing, and rational. It is unclear, however, if Cavendish can actually dispense of atomism. One of her arguments against atomism, for example, depends upon the created world being harmonious and orderly, a premise Cavendish herself repeatedly undermines by noting nature’s many disorders. I argue that her supposed difficulties (...) with atomism expose a deeper tension in her work between two fundamental metaphysical commitments each of which has substantial philosophical support: her monist theory of the material world (which maintains that there exists just one natural substance which is the single principal cause) and her occasional theory of causation (which requires multiple finite principal causes in nature -- causes that might be considered individual substances). Her monism undermines atomism while her theory of occasional cause seems to rest on a conception of nature that would be especially friendly to atomism. I argue further that we can solve this tension within a Cavendishian framework in such a way as to preserve her theory of causation and her monism, but that this solution depends upon our taking her monism in a particular (and weak) form. I finally note that we can best make sense of her unique and interesting form of monism by acknowledging her social-political motivations in addition to her motivations in natural philosophy. (shrink)

THE MAJOR PREMISE OF DUNS SCOTUS'S IMPRESSIVE PROOF FOR THE EXISTENCE OF GOD HAS BEEN NEGLECTED. THAT PREMISE, "THE MOST PERFECT BEING IS INFINITE," IS ESTABLISHED IN TWO WAYS. THE KEY PREMISE IN EACH WAY IS THE PROPOSITION, "POSSIBLY, SOME BEING IS INFINITE." THIS PROPOSITION CANNOT BE PROVEN TO BE TRUE, NOT BECAUSE IT IS IN ANY WAY DUBIOUS OR LACKING IN EVIDENCE, BUT BECAUSE ITS TERMS ARE SIMPLE AND NOT SUBJECT TO PROOF OR FURTHER ANALYSIS. BEING (...) IS THE SIMPLEST AND MOST IMMEDIATE OF CONCEPTS; AND BEING INFINITE IS SIMPLY THE NEGATION OF BEING FINITE. INSTEAD OF PROOF, SCOTUS PRESENTS "PERSUASIONES", SKETCHES OF LANGUAGE-GAMES TO SHOW THAT THE PROPOSITION IS TRUE. (shrink)

In the corollaries to Book I, Chapter 5 of De causa Dei, Thomas Bradwardine assumes the existence of an actual, infinite, God-filled extramundane void. Thomas Buckingham, Bradwardine’s former student, develops in the unedited Question 23 of his Quaestiones theologicae a rejection of the void’s existence precisely in opposition to the theory of his master. His argumentation is not only remarkable in its own; it also allows us to reassess essential concepts from Bradwardine’s De causa Dei, such (...) as divine power, causality and ubiquity. This paper first presents the Aristotelian notion of the void in rendering it in the context of the philosophy of nature at fourteenth-century Oxford; it is then dedicated to the analysis of the chapter in question from De causa Dei along with Buckingham’s answer. It is accompanied by a critical edition of Question 23 from Buckingham’s Quaestiones theologicae, »Utrum sit necesse ponere Deum esse extra mundum in situ seu vacuo imaginario infinito«. (shrink)

The Meaning of Evil is one of the most profound yet accessible books written on this immensely important, (and never more timely) topic. Deeply immersed in the highest traditions of realist philosophy and theology, Journet addresses the truly important issues surrouding the nature of evil and the burning questions demanded of us by its existence and (on occasion) seeming dominance in our world. Topics addressed include: definitions of evil throughout history; the actual forms of evil?including the two forms (...) of evil in man; and the inescapeable questions: ?Does evil come from God?? ?Is God responsible for Sin?? and ?What is God bound to do in his infinit goodness? as a consequence? Journet also discusses the temptation to suicide and the right attitude toward evil; and, finally, why the existence of evil actually proves, not disproves, the existence of an all-good God.This republication of "The Meaning of Evil" (first published in English in 1963) also contains, as an extended introduction, a major re-assessment of Journet and his impressive corpus of work, as well as a theoretical treatment of Journet?s concept of evil in the universe and as an ever-present element in the human condition. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 44.2 (2006) 321-322 [Access article in PDF] Thomas Holden, The Architecture of Matter: Galileo to Kant. Oxford: Clarendon Press, 2004. Pp. x + 305. Cloth $74.00. Most scholars believe that the problem of infinite divisibility that plagued early modern natural philosophy was an entirely mathematical issue and, therefore, resulted from the short-comings of early modern mathematics. Accordingly, advances in geometry, topology and (...) the logic of infinity are often thought to lay this debate to rest, thereby reducing it to some quaint footnote in the history of natural philosophy. Thomas Holden, however, through thorough textual and philosophical analysis, convincingly argues that this debate was more metaphysical in nature than previously supposed. He shows how the various paradoxes concerning the structure of matter stem from two widely-accepted theses central to the new science. The first resulted from the early modern method of applying the principles of geometry to physics. This geometrical method dictated that bodies are metaphysically divisible (m-divisible) in infinitum, because they occupy regions of space that can, at least by the power of God, be subdivided into those parts occupying corresponding sub-regions of space, and those sub-parts into those sub-sub-parts occupying their respective corresponding sub-sub-regions of space in infinitum. The other thesis is that "the parts of material bodies are each concrete existents in their own right" (3). Such actual parts exist prior to any act of division, whereas parts that are only potential would not exist prior to division but only after a divisive act has occurred. Holden argues that the actual parts doctrine was a metaphysical thesis just as fundamental to Enlightenment natural philosophers as the geometrization of matter. Indeed, it is these two theses that came into conflict and gave rise to a plethora of antimonies at the heart of the new science.Holden should be applauded for the skill he employs in challenging the received scholarship. In chapter 1, after some historical and terminological preliminaries, Holden reconstructs several of the more popular paradoxes of material structure found throughout the period's vast literature and successfully shows how these paradoxes would not arise if the problems of material structure were merely mathematical. He shows how the metaphysical doctrine of actual parts gave rise to these difficulties because of its conflict with the assumed geometrical doctrine that extension is infinitely m-divisible. For example, some thought it followed from the actual parts doctrine that there must be an actual infinity of parts, because actual parts exist prior to any process of division and, therefore, in order for both actual parts and infinite m-divisibility to be true, there must be an actual infinity of parts. This raised issues about the intelligibility and piety of an actual infinite as well as issues about equal and unequal infinities, e.g., half an infinite number of parts would still be infinite but half as much as the whole collection of parts. Hence, this and other paradoxes would not arise in the absence of the actual parts doctrine, and so the debate is more metaphysical in nature than previously supposed. [End Page 321]Chapter 2 examines in more detail the actual parts metaphysic and how it leads to tension with infinite m-divisibility. Chapter 3 examines various "short-circuit" arguments designed to undermine the actual parts doctrine. And chapter 4 examines the actual parts doctrine via the argument from composition found in Kant's pre-critical work, Physical Monadology. In chapter 5, Holden briefly examines the potential parts doctrine and how some actual-parts partisans tried to undermine it. It is eventually concluded that actual-parts and potential-parts advocates are at an impasse due to the question-begging nature of their respective arguments. Finally, chapter 6 is "something of an addendum" (74), since it examines a fascinating synthesis of the two conflicting positions, viz. the Kant-Boscovich force-shell atom theory.Given that the book is about material structure, it is a propos that my critical comment is about the structure of the book. It seems... (shrink)

In line with much current literature, Bradley’s regress is here discussed as an argument that casts doubt on the existence of states of affairs or facts, understood as complex entities working as truthmakers for true sentences or propositions. One should distinguish two versions of Bradley’s regress, which stem from two different tentative explanations of the unity of states of affairs. The first version actually shows that the corresponding explanation is incoherent; the second one merely points to some prima facie (...) implausible consequences of the explanation it stems from, e.g., that there are infinite explanatory chains and that, for any given fact, there are infinitely many facts involving exemplification relations of increasing levels. But these consequences can be swal- lowed after all, thereby leading to the acceptance of a doctrine which may be called fact infinitism, a doctrine adumbrated in a well-known discussion of relations by Meinong. (shrink)

Wes Morriston argues that even if we take an endless series of events to be merely potentially, rather than actually, infinite, still no distinction between a beginningless and an endless series of events has been established which is relevant to arguments against the metaphysical possibility of an actually infinite number of things: if a beginningless series is impossible, so is an endless series. The success of Morriston’s argument, however, comes to depend on rejecting the characterization of an endless (...) series of events as a potential infinite. It turns out that according to his own analysis it is vitally relevant whether the series of events is potentially, as opposed to actually, infinite. If it is reasonable to maintain that an endless series of events is potentially infinite while a beginningless series is actually infinite, then a relevant distinction has been established for any person who thinks that an actual infinite cannot exist. (shrink)

Existence monism (EM) is a metaphysical view asserting the existence of only one concrete object. EM is well known for its radicalness, and encounters difficulty in terms of its prima facie inconsistency with truisms. This paper aims to propose an alternative (and somewhat easy) way to overcome this difficulty and indicate another means by which the possibility of EM can be defended. I will present a package of theses that are intended to be combined with EM, which I (...) call Linguistic Ontology with the One as Semantic Glue (LOOSG). I will show that this package (in combination with EM) provides a systematic explanation as to why truisms hold while only one concrete object actually exists. In other words, I will argue that if an existence monist embraces LOOSG, the desired explanation for truisms is then available to her. In addition, it will also be noted that LOOSG has a theoretical virtue, in that it only presupposes the framework of standard semantics. Based on these discussions, I offer LOOSG as a viable option for existence monism. (shrink)